DeSmuME attempts to emulate, as faithfully as possible, the Nintendo DS and Nintendo DS Lite handheld game consoles (NDS). It currently runs on Windows, Linux, and Mac OS X.
DuoS is a Nintendo DS emulator with sound and save states.
The few games I tested played well with no major problems.
melonDS aims at providing fast and accurate Nintendo DS emulation. While it is still a work in progress, it has a pretty solid set of features...
NeonDS is a Nintendo DS Emulator. Compatibility is good and most games have playable speed. No Audio at the moment but this emulator has come a long ways in a very short time.
(Discontinued)
NooDS aims to be a fast and portable Nintendo DS emulator. It's not quite there speed-wise, but it offers most other features that you might expect from a DS emulator. It even supports GBA backwards compatibility!
3 out of 4 random games I tested played well. I did have to run the emulator as administrator, otherwise games ran too slow to be playable.